We show that for random bit strings, Up(n), with probability, p = 1 2 , the firstorder quantifier depth D(Up(n)) needed to distinguish non-isomorphic structures is (lg lg n), with...
We propose a definition of locality for properties of geometric graphs. We measure the local density of graphs using region-counting distances [8] between pairs of vertices, and w...
The goal is to build a general framework for ad hoc applications over large networks using semantics and complex systems analysis. The first part deals with semantics because appl...
For automatic and recursive graphs, we investigate the following problems: (A) existence of a Hamiltonian path and existence of an infinite path in a tree (B) existence of an Euler...
It is well-known that inference in graphical models is hard in the worst case, but tractable for models with bounded treewidth. We ask whether treewidth is the only structural cri...